how to make absolut value in python model

Answered

Rahadyan Bagus P

January 04, 2024 04:44

i want to change G[i,j] into | X[i] - X[j] |

model.setObjective(grb.quicksum(Cobj[i,j]*G[i,j] for i in N for j in N if i<j))

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Official comment
Simranjit Kaur

Gurobi Staff

November 13, 2026 01:32
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Jaromił Najman

Gurobi Staff

January 04, 2024 08:12 Edited
You can use the addGenConstrAbs method to do that. You will have to formulate

\[\begin{align*}
z_{ij} &= X_i - X_j\\
G_{ij} &= |z_{ij}|
\end{align*}\]

or in Python (pseudo code)
```
# add a free auxiliary variable to the model
z[i,j] = model.addVar(lb=-GRB.INFINITY, name="z"+str(i)+str(j))
# add constraint z_ij = X_i - X_j
model.addConstr(X[i] - X[j] == z[i,j], name="aux_constr_"+str(i)+str(j))
# add constraint G_ij = |z_ij|
model.addGenConstrAbs(G[i,j], z[i,j], "absconstr_"+str(i)+str(j))
```
Note that it is necessary to introduce an auxiliary variable \(z_{ij}\) because the addGenConstrAbs method accepts only single optimization variables as input arguments. Moreover, it is necessary to define the lower bound of \(z_{ij}\) as \(-\infty\) because the default variable lower bound in Gurobi is \(0\).

Best regards,
Jaromił
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